# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2020 | Feb-Mar | (P1-9709/12) | Q#8

**Question**

A woman’s basic salary for her first year with a particular company is $30000 and at the end of the year she also gets a bonus of $600.

**a)**For her first year, express her bonus as a percentage of her basic salary.

At the end of each complete year, the woman’s basic salary will increase by 3% and her bonus will increase by $100.

**b)**Express the bonus she will be paid at the end of her 24th year as a percentage of the basic salary paid during that year.

**Solution**

From the given information, we can collect following information.

The basic salary for her first year;

The bonus at the end of first year;

**a)
**

Her bonus as percentage of her salary;

Her bonus is 2% of her first year’s salary.

**b)**

Salary of 1^{st} year;

Since annual rate of growth continues to be constant at 3%.

Salary of 2^{nd} year;

Similarly, salary of 3^{rd} year will be;

Hence, salary for 4^{th} year will be;

It is evident that this model represents Geometric Progression (G.P).

Now, we find her salary on 24^{th} year.

Expression for the general term in the Geometric Progression (G.P) is:

Therefore;

We can find the common ratio as follows.

Expression for Common Ratio () in a Geometric Progression (G.P) is;

Hence;

Hence;

Her bonus on 24^{th} year will be;

Finally, we can express this bonus as percentage of 24^{th }year’s salary;

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